PMLs: A direct approach

Abstract

This brief article outlines a new and rather simple method for obtaining the finite element matrices for a perfectly matched layer used for elastic wave propagation in the context of a frequency-domain formulation. For this purpose, we introduce a fairly mild simplification, which allows applying the stretching functions directly to the mass and stiffness matrices obtained via conventional methods (i.e., elastic elements), a novel strategy that allows circumventing the use of integration via Gaussian quadrature. In essence, the technique proposed herein is equivalent to a direct application of the method of weighted residuals in stretched space, followed by a conversion of the linear dimensions into position-dependent complex-values. Most importantly, numerical tests demonstrate that the technique does work as intended, and in fact, splendidly so.